Around Sziklai's conjecture on the number of points of a plane curve over a finite field

초록

This paper has double purposes. One of them is to give a new bound on the number of points of a plane curve of degree d over a finite field that meets Sziklai's conjectural bound at d = q + 1. An example shows that this bound is sharp for d = q + 1. The second one is to Study an example against that conjecture for q = d = 4. This curve also shows the sharpness of our bound. (C) 2009 Elsevier Inc. All rights reserved.

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